AN EXPLANATION OF THE FALSE SPECTRA FROM 

 DIFFRACTION GRATINGS. 



By Thkodoke Lyman. 



Presented May 13, 1903. Received May 27, 1903. 



In a previous paper * the author has shown that the principal spectra 

 produced by concave diffraction gratings are complicated by the presence 

 of false spectra of lower order than the first, and that these false spectra 

 are common and often of excellent definition. It is the purpose of this 

 paper to show that these false spectra are not of the nature of " ghosts," 

 and that, while the theories developed to explain the latter cannot be 

 made to fit them, a theory proposed by Professor Carl Runge, after 

 examining one of the plates which formed the basis of the earlier paper, 

 furnishes an explanation of the phenomena. 



The " ghost," so called, is a faint reproduction of a real line, and in 

 general occurs within a few Angstrom units of its parent. The false 

 spectra not only occur in regions many hundred units from that occupied 

 by the principal line, but also differ fundamentally from " ghosts " in 

 other respects. 



Mr. C. S. Pierce t has made a careful mathematical study of the sub- 

 ject, and his paper also contains experimental data on the position of 

 " ghosts," showing a good agreement between the theory and the observed 

 facts. His treatment, however, deals only with " ghosts " occurring very 

 near the parent line. Rowland \ has given a theory, the formulae of 

 which jnay be extended to the case of false lines occurring at a consider- 

 able distance from the parent. The author, however, has never been 

 able to fit the positions or intensities of any of his observed false spectra 

 into these formulae in the form given by Rowland. In the case of most 

 gratings this does not seem surprising, since the false spectra are very 

 numerous, of small intensity, and with wave-lengths which bear no simple 



* These Proceedings, 36, No. 14. 



t American Journal of Math.. 2, 330 (1879). 



| Rowland's Physical Papers, p. 525. 



